Reimer turned aside 43 shots and Kessel hit the net in the first and second period with assists from Nazem Kadri, who chipped in a goal of his own in the third period with an assist from Kessel.
The victory was Toronto's third in their last four games. Edmonton has lost their last four.
Richard Bachman made 22 saves for Edmonton.
Celebrity Families of 2014 [PHOTOS]